1. Field of the Invention
The invention relates to petroleum reservoir exploration and development, and more particularly to petroleum reservoir imaging. Constructing images representative of the subsoil and compatible with data measured in wells and/or with the entire reservoir favors the development of such reservoirs.
2. Description of the Prior Art
Studying a petroleum field requires constructing models referred to as “geological models” in a broad sense. These models, which are well known and widely used in the petroleum industry, allow determination of many technical parameters relative to prospecting, study or development of a reservoir, and of hydrocarbons. In fact, the geological model is representative of the structure of the reservoir and of the behavior thereof. It is thus possible to determine which zones are the most likely to contain hydrocarbons, the zones in which it can be interesting/necessary to drill an injection well in order to enhance hydrocarbon recovery, the type of tools to use, the properties of the fluids used and recovered, etc. These interpretations of geological models in terms of “technical development parameters” are well known, even though new methods are regularly developed. It is therefore crucial, in the petroleum field, to construct a model as precise as possible. Integration of all the available data is therefore essential.
Petroleum reservoirs are generally very heterogeneous and fractured media. Modelling a reservoir which is constructing a geological model representative of the reservoir, requires construction methods referred to as “probabilistic” due to the limitation of available information (limited number of wells, etc.). The geological models constructed from these probabilistic methods are therefore referred to as “stochastic models”. Construction of a stochastic reservoir model first has to depend on the environment of the geological deposit, which allows representation of the major heterogeneities controlling the flow of fluids. A model then has to be constrained by quantitative data, such as core data, log data, seismic data, which allows a further increase of the reliability of the model for production prediction.
A geological model is a model of the subsoil, representative of both its structure and its behavior. Generally, this type of model is represented on a computer, which is referred to as a numerical model. In two dimensions (2D), it is referred to as a map. Thus, a map corresponds to an image of pixels with each pixel containing information relative to the behavior of the subsoil being studied (a petroleum reservoir for example). These pixels correspond to a precise geographic position and are located by coordinates. When values are assigned to a pixel, by simulation for example, it is referred to as a simulation point. The representative image (map or model) is generated on any medium (paper, computer screen, etc.).
The images obtained from multi-Gaussian type methods or, more generally, from pixel type methods affords the advantage of being more readily constrained by quantitative measurements. However, the drawback of such methods is that they are difficult to account for the geological concepts. The term “geological concept” designates the physical rules of sedimentation in each type of depositional environment.
On the other hand, images obtained from object type methods and from genetic type methods (based on sedimentary processes) allow better accounting for the geological architecture. However, constraining them by quantitative measurements is often more difficult to achieve.
Simulation type image construction methods using multipoint statistics allow this problem to be solved. In fact, models generated by object or genetic type simulation provide non-constrained images that can be used as training images for multipoint statistics inference. On the basis of these statistics, it is then possible to regenerate images pixel by pixel, using a sequential simulation algorithm. These images reproduce the main characteristics of the images obtained from object or genetic type methods. The flexibility of sequential simulation for conditioning to quantitative data is an additional asset. The multipoint geostatistical approach is first developed within a stationary context where the spatial variability of the reservoir heterogeneity is assumed to stabilize beyond a certain distance, markedly smaller than the size of the field. This approach is described in the following documents:    Guardiano, F. and Srivastava, M. (1993): Multivariate Geostatistics: Beyond Bivariate Moments. In Soares, A., ed., Geostatistics Troia'92, vol. 1: Kluwer Acad. Publ., Dordrecht, The Netherlands, p. 133-144;    Strebelle S. and Journel, A. (2000): Sequential Simulation Drawing Structures from Training Images. In Kleingeld and Krige (eds.), Geostatistics 2000 Cape Town, Volume 1.
Now, in most cases in practice, the heterogeneity is non stationary on the scale of the petroleum field being studied. This non-stationary variability is often accessible via information, from seismic data for example, of low resolution but covering the entire field.
There are also known methods allowing accounting for this information referred to as auxiliary in a simulation by the multipoint approach.
A first method uses, in addition to a training image of the principal variable, a second training image of the auxiliary variable. The latter is obtained by numerical simulation on the former. For a given state of a neighborhood of points of the principal variable and a datum of the auxiliary variable at the simulation point, all the point configurations coherent with both the state of this neighborhood and this auxiliary datum are identified and the empirical law of the principal variable at the simulation point, conditioned by both the state of this neighborhood and the auxiliary datum, is obtained. This method, which is quite direct and coherent, however involves a major drawback. In fact, due to the often continuous character of the auxiliary variable, it is generally unlikely to find a configuration, in both training images, which coincide with both the state of a given neighborhood and a datum of the auxiliary variable. One way of dealing with this difficulty is to classify the auxiliary variable into several classes, which makes the method somewhat arbitrary while only slightly mitigating the problem. The following document describes the various aspects of this method:    Strebelle S. (2000): Sequential Simulation Drawing Structures from Training Images. Ph.D. Thesis, Department of Geological and Environmental Sciences, Stanford University.
Another method based on an analytical model, the “tau model”, is described in:    Journel A. G. (2002) Combining Knowledge From Diverse Sources: An Alternative to Traditional Data Independence Hypotheses. Math. Geology, Vol. 35, N. 5.
The use of this method for non-stationary multipoint simulation is notably described in:    Strebelle S., Payrazyan K., Caers J. (2002): Modeling of a Deepwater Turbidity Reservoir Conditional to Seismic Data Using Multiple-Point Geostatistics. SPE 77425.
This method permits expression of the probability of an event denoted by A knowing the events denoted by B and C as a function of the probability of A and those of A knowing B and C respectively. Using this method in the non-stationary multipoint simulation calculates the probability of A (presence of a lithology at the simulation point) knowing B (state of a lithology neighborhood) and C (given value of the auxiliary variable) as a function of the probability of A (global lithology proportion), the probability of A knowing B (from the training image of the auxiliary variable) and the probability of A knowing C (from the auxiliary constraint). This function depends on a “tau” parameter. The difficulty in using this method in practice comes from the inference of this parameter, which depends not only on each reservoir but also on each simulation point of a reservoir. In the current use of this method, “tau” is simply assigned to value 1. The degree of approximation of such an assignment is difficult to evaluate.
The previous two methods, that is the classification algorithm and the tau model, show geometrical artifacts without reproducing the non-stationary constraints. A third non-stationary multipoint simulation method is disclosed in French Patent 2,905,181 or from the following publication: Chugunova, T. and Hu, L. Y. (2008)” Multiple-point Simulations Constrained to Continuous Auxiliary Data, Mathematical Geosciences, Vol. 40, No. 2. This method avoids the drawbacks of the previous two algorithms by integrating continuous spatial constraints. However, this method is limited because it does not account for several auxiliary constraints. Now, in common practice, where multiple auxiliary constraints are generally available, all of these data are preferably accounted for in the quality of the petroleum reservoir image obtained.